Left is the Governor of Hong Kong, Sir Henry Arthur Blake GCMG DL JP FRGS, he was appointed from 25. November 1898 – 21. November 1903.
On the right is the representative of the Chinese Empire, the “Viceroy of Canton” as referred in the British reports – his name is not mentioned there (for whatever reason?). Wikipedia gives the correct title as Viceroy of Liangguang (full title: Governor-General, Commander and Quartermaster, Supervisor of Waterways, and Inspector-General of the Two Expanses and Surrounding Areas). His name was Tan Zhonglin (Chinese: 譚鍾麟; Wade–Giles: T'an Chung-lin, he was viceroy from 16. April 1895 to 19. December 1899.
There is a photo of both, probably taken during the visit of Governor Blake in Canton on the 2. April 1899.
For the story behind this photo see: The Anglo Chinese Boundary 1898